Ray inverters for minimizing delay distortion in multimode optical fibers

ABSTRACT

Delay distortion, due to differences in the group velocities of the various modes propagating along a multimode optical fiber, is minimized by the inclusion, along the fiber, or an array of three, equally spaced, converging lenses for inverting the order of the rays representing the various modes. The first and the third of said lenses, whose focal lengths are F/2, have their optical centers located a distance F from the ends of the adjacent fibers, and a distance F( theta &#39;&#39;max/2) from the fiber axis, where theta &#39;&#39;max is the maximum angle at which energy is radiated by the fiber. The center lens, whose focal length is F, is equally spaced a distance F from each of the other two lenses, and has its optical center on the guide axis. The physical configuration of the lenses depends upon the radiation pattern at the end of the particular fiber used.

H SR -3 0759 e590 [111 3,759,590 [451 Sept. 18, 1273 RAY INVERTERS FORMINIMIZING DELAY DISTORTION IN MULTIMODE OPTICAL FIBERS Inventor:Jacques Alexis Araand, Colts Neck,

Assignee: Bell Telephone Laboratories,

Incorporated, Murray Hill, Berkeley Heights, NJ.

Filed: Sept. 11, 1972 Appl. No.: 288,032

US. Cl. 350/X6 WG, 350/54, 350/167,

' 350/190, 350/191 Int. Cl G021: 5/14, G021: 27/00 Field of Search350/96 WG I, References Cited UNITED STATES PATENTS 8/1965 Goubau 350/96WG 9/1969 [to 350/96 WG UX 10/1971 Martin et al. 350/96 WG PrimaryExaminer-John K. Corbin Attorney-W. L. Keefauver [57] ABSTRACT Delaydistortion, due to differences in the group velocities of the variousmodes propagating along a multimode optical fiber, is minimized by theinclusion, along the fiber, or an array of three, equally spaced,converging lenses for inverting the order of the rays representing thevarious modes. The first and the third of said lenses, whose focallengths are F/2, have their optical centers located a distance F fromthe ends of the adjacent fibers, and a distance F(6',,..,,/2) from thefiber axis, where 03,." is the maximum angle at which energy is radiatedby the fiber. The center lens, whose focal length is F, is equallyspaced a distance F from each of the other two lenses, and has itsoptical center on the guide axis. The physical configuration of thelenses depends upon the radiation pattern at the end of the particularfiber used.

3 Claims, 10 Drawing Figures PATENTED 35? I 3I973 SIfEI 1 II 3 OPTICALSIGNAL RECEIVER RAY INVERTER uni-J T OPTICAL SIGNAL SOURICE FIG 4PATENTEB SE?! 8 I973 SHEET 2 0F 3 FIG. 6

FIG. 7

NCORRECTED OUTPUT PU/LSE CORRECTED OUTPUT PULSE TIME DTITV gTT TKI/INPUT PULSE PATENTED SEP] 8 I975 saw 3 or 3 FIG /0 RAY INVERTERS FORMINIMIZING DELAY DISTORTION IN MULTIMODE OPTICAL FIBERS The inventionrelates to delay equalizers for use with multimode optical fibers.

BACKGROUND OF THE INVENTION Recent advances in the fabrication ofultratransparent materials have demonstrated that fibers are a promisingtransmission medium for optical communication systems. By using coherentsources and single mode fibers, such systems are theoretically capableof operating at pulse rates of the order of tens of gigahertz.

There are, however, many applications which are preferably optimizedwith respect to cost and simplicity, rather than speed. Systems of thislatter kind would employ incoherent light sources and multimode fibers.

In the copending U.S. Pat. application by E. A. J. Marcatili, Ser. No.247,448, filed Apr. 28, I972, there is described an arrangement forcoupling an incoherent signal source to a multimode fiber. As notedtherein, one of the problems associated with such systems is the delaydistortion resulting from the fact that the various modes propagatealong a multimode fiber with different group velocities. While means aredisclosed by Marcatili for reducing this distortion, it cannot betotally eliminated.

It is, accordingly, the broad object of the present invention tominimize the delay distortion produced in multimode optical fibers.

SUMMARY OF THE INVENTION As is known, in a multimode optical fiber eachof the various propagating modes can be characterized by means of a rayprogressing along the fiber at a specific angle to the fiber axis. Inparticular, the higher order modes propagate at larger angles to theaxis and, hence, have a lower resultant propagation velocity along thedirection of the fiber axis. Conversely the lower order modes propagateat smaller angles and at correspondingly higher velocities.

In accordance with the present invention, the delay distortion, due todifferences in the group velocities of the various modes, is minimizedby the inclusion, along the fiber, of an array of three lenses forinverting the order of the rays. Thus, a ray entering the inverter at alarge angle is transformed into a small angle ray, while a small angleray is transformed into a large angle ray. More generally, a ray makingan angle with the fiber axis is transformed into a ray at approximatelyan angle 0,, 0, where 0, is the maximum angle that a guided mode makeswith the fiber axis. The net effect is to convert the energy in thefaster propagating modes into slower propagating modes, and to convertthe slower propagating modes into faster propagating modes, such thatall the energy propagates more nearly at the same average groupvelocity.

Each of the specific embodiments to be described comprises an array ofthree, equally spaced converging lenses. The first and the third of saidlenses, whose focal lengths are F/2, have their optical centers locateda distance F from the ends of the adjacent fibers, and a distance F0' /2from the fiber axis, where 0' is the maximum angle at which wave energyis emitted at the end of the fiber. The center lens, whose focal lengthis F, is equally spaced a distance F from each of the other two lensesand has its optical center on the axis.

The physical configuration of the lenses depends upon the fiber used. Inone embodiment, using a ribbon fiber that is multimode in only one ofits transverse directions, cylindrical lenses for focusing along theplane of the fiber are used. In a second embodiment of the invention,using a multimode circular fiber, lenses having circular symmetry areused.

These and other objects and advantages, the nature of the presentinvention, and its various features, will appear more fully uponconsideration of the various illustrative embodiments now to bedescribed in detail in connection with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. I shows, in block diagram, anoptical communication system in which the present invention is employed;

FIG. 2 shows the ray orientation for one embodiment of a multimodetransmission line for use in an optical communication system of the typeillustrated in FIG. 1;

FIG. 3 illustrates the principle of operation of a ray inverter inaccordance with the present invention;

FIG. 4 shows, in greater detail, structural features of two of thelenses used in the ray inverter;

FIG. 5 shows, in perspective, the details of a ray inverter for use withthin ribbon fibers;

FIG. 6 shows the radiation field at one end of a circular core,multimode optical fiber;

FIG. 7 shows, in perspective, the details of a ray inverter for use witha circular core fiber;

FIG. 8 shows the effects of delay distortion on an input pulse, and theimprovement to be realized by using a ray inverter in accordance withthe present invention; and

FIGS. 9 and 10 show, by way of example, two ways in which a ray invertercan be fabricated.

DETAILED DESCRIPTION Refen'ing to the drawing, FIG. 1 shows, in blockdiagram, an optical communication system comprising an optical signalsource 10, an optical signal receiver 11, and a multimode optical fibertransmission line 12 coupling the source to the receiver. A ray inverter13, to be described in greater detail hereinbelow, is located alongtransmission line 12 and serves to minimize the delay distortion at thereceiver 11. While only one inverter is shown, more can be used. If moreare considered necessary, an odd number of inverters, equally spacedalong line 12 would be employed.

The present invention relates particularly to the transmission lineportion of the system, and to means for equalizing the delay distortionalong the line. In this regard, reference is now made to FIG. 2 whichshows a portion of line 12 and, in partieular, an optical fibercomprising a thin, ribbon-like inner core 14, surrounded by a cladding15 of lower refractive index. The narrow dimension 1 of core 14 isselected such that the fiber is supportive of only the fundamental, orlowest order mode along the narrow dimension of the guide. The widedimension w, on the other hand, is much greater than t such that itsupports a plurality of modes. For purposes of explanation, two rays 1and 2 are illustrated in FIG. 2, wherein one of the lower order modes,represented by ray 1, is shown propagating at a very small angle 0 tothe fiber axis 2-2, and a higher order mode, represented by ray 2, isshown directed at a relatively larger angle 0, to the axis. (Typically,the ray'angles would lie within a range between 0.l and Both rays arereflected at the core-cladding interface and, hence, are guided alongthe fiber. Any higher order modes, whose angles of incidence at theinterface are less than critical, are not reflected, and tend to radiateout of the fiber. The maximum ray angle 0, for a guided mode is given byVEK is given by where n, denotes the refractive index of the surroundingmedium.

lf n n we have The relative delay, t, between any of the higher ordermodes and the fastest mode is given by t= (nL/2c) 0 where L equals theline length;

c is the vacuum velocity of light; and

6 is the ray angle for the particular mode.

From the above, it is apparent that, in the absence of corrective means,components of wave energy associated with the various modes propagatingalong a multimode fiber will arrive at the output end of thetransmission line at different times. In the copending US. Pat.application by S. E. Miller and S. D. Personick, Ser. No. 75,383, filedSept. 25, 1970, assigned to applicants assignee, it was noted that delaydispersion can be minimized by deliberately introducing imperfections"along the fiber so as to enhance the mode-tomode coupling. This has theeffect of converting the .energy associated with the faster propagating,lower order modes into slower propagating, higher order modes and viceversa. The net result is that all of the energy tends to propagate atapproximately the same average group velocity and arrives at the outputend of the transmission line at approximately the same time.

The present invention achieves essentially the same result but bydiscrete means disposed along the optical wavepath rather than bymodifying the transmission characteristics of the optical fiber itself.In particular,

means are provided for inverting the mode order so that the fasterpropagating modes are converted into slower propagating modes, and theslower modes are converted into faster modes.

FIG. 3, now to be considered, illustrates the principle of operation ofa ray inverter in accordance with the present invention. Basically, theray inverter comprises an array of three, equally spaced converginglenses 30, 31 and 32 disposed between the ends of a pairoflongitudinally spaced, coaxially aligned optical fibers 33 and 34.With reference to FIG. 1, fibers 33 and 34 are merely adjacent segmentsof transmission line 12.

Each of the lenses 30 and 32 comprise two identical sections, 30', 30"and 32', 32", symmetrically disposed with respect to the fiber axis ZZ.This derives from the symmetry of the radiation pattern at the end ofthe fibers, as shown in FIG. 2. In the discussion that follows,reference will be made to only one of the lens sections, it beingunderstood that such reference is equally applicable to both.

Lens sections 30 and 32 are converging lenses of focal length F/2, whosecenters, 0 and c, are located a distance F from the nearest adjacentfiber and a distance F0' /2 from the fiber axis ZZ. Points 0, b, and d,e are, respectively, the focal points of lenses 30' and 32'.

The center lens 31 is also a converging lens, but of focal length F Lens31 is equally spaced a distance F from each of the other lenses, andpositioned with its optical center g along the ZZ axis. The focal pointsh and k of lens 31 lie along the fiber axis.

For purposes of explanation, two rays 3 and 4, emitted at the output endof fiber 33 are identified in FIG. 3. Ray 3, associated with the lowerstorder mode, makes an extremely small angle 0 with the fiber axis. Ray 4,on the other hand, representing the highest order mode, makes themaximum angle 0,, with the fiber axis. An insignificant amount of waveenergy, directed along the axis, is essentially unaffected by the lenssystem. Ray 3, however, which is directed at a small angle to the fiberaxis, is deflected by lens section 30, passes through focal point b, andis redirected by lens 31 along a path that is essentially parallel tothe fiber axis. Upon traversing lens section 32, ray 3 is deflected soas to pass through focal point e, and into fiber 34 at an angle which isessentially equal to 0 Ray 4, representing the highest order mode passesthrough focal point a of lens section 30', and is deflected by thelatter along a direction that is essentially parallel to the fiber axis.Upon traversing lens 31, ray 4 is deflected such that it passes throughfocal point d of lens section 32', and is then redirected by the latterso that it enters fiber 34 at a small angle approximately equal to 0 Itwill be noted that the mode order has been inverted such that ray 4,representing wave energy associated with the slowest propagating mode,has been redirected by the lens array, and now represents wave energyassociated with one of the fastest propagating modes. Conversely, ray 3representing the fastest propagating mode is converted into the slowestpropagating mode. Similarly, all the intermediate modes are likewiseinverted such that a mode, entering the lens system at an angle 0, isinverted so that it leaves the system at an angle 0,, 0, and vice versa.

While no mention was made of the size of the several lenses, it isapparent that each should be sufliciently large to intercept all of theenergy radiated by the input fiber. Thus, each lens should extend atleast a distance FO' above and below the fiber axis. In FIG. 3, thediameters of lens sections 30 and 30" of lens 30, and lens sections 32and 32" of lens 32, are shown to be just equal to the minimum specified.Advantageously, however, the lens sections should be made larger thanthe minimum for structural reasons. For example, in FIG. 3 the lenssections are shown meeting at a point at the axis. By making themlarger, as illustrated in FIG. 4, they will have some finite thicknessalong the axis, resulting in a stronger structure. The dotted lensportions, shown in FIG. 4, represent that portionof each lens sectionwhich merges into the other since the optical centers of the two lenssections remain at a distance F 0' /2 from the fiber axis in all cases.

Using the same identification numerals as in FIG. 3, the ray inverterfor a ribbon fiber transmission line is shown in perspective in FIG. 5.Since, as explained hereinabove, the ribbon fiber is multimode in onlyone of its transverse dimensions, delay equalization is only requiredalong the one direction. Hence, each of the lenses 30, 31 and 32 can bea cylindrical lens which provides the above-described focusing action inonly the plane of the fiber core, while confinement of the beam in thenarrow dimension is insured by the continuation of the fiber corematerial and the cladding material throughout the system.

Thus, each of the lenses 30 and 32 comprises two identical lens sections30', 30 and 32', 32", symmetrically disposed to either side of the fiberaxis. The optical center of each lens section lies along a lineperpendicular to the wide dimension of the fibers at a distance F0,, ,/2from the axis.

Lens 31 comprises a single section lens whose optical center lies alonga line which passes through the fiber axis along a directionperpendicular to the wide dimension of the fiber.

The region between lenses, and between the fibers and the lenses isfilled with core material 35, surrounded by cladding material 36, forguidance along the narrow dimension of the fiber. The lenses, embeddedas they are within the core material, would be made of a material havinga higher refractive index than the core material.

In the more general case of a circular core optical fiber, such as isillustrated in FIG. 6, the symmetry of the core 16 is such that thefiber is multimode along all transverse directions. In this latter case,the radiation field at the end of the fiber is concentrated with thecone formed by the highest order propagating mode. Thus, lenses 30, 31and 32 must have circular symmetry in order to redirect the cone of raysrepresenting each of the propagating modes. For this more general case,the arrangement shown in FIG. 3 is merely an axial cross-section of thecomplete lens system which is formed by rotating the lens sections shownabout the axis Z-Z. The resulting three dimensional lens system, shownin perspective in FIG. 7, comprises two toroidallike lenses 50 and 52,of focal lengths F/2, whose physical centers lie along the fiber axisand whose optical centers lie along a circle of radius F0',,,.,/2. Thethird lens 51 is a spherical lens, of focal length F, whose physical andoptical centers lie along the fiber axis.

It is important to note that in the above-described arrangements, theend of fiber 33 is imaged with magnification unity, onto the end offiber 34 and, consequently, no ray is lost in principle. (This isstrictly true only for a point on the fiber axis. However, because thefiber core is so much smaller than the lenses, it is approximately truefor all points on the core.) Another interesting feature of the systemis that it is free of coma aberration and distortion as a result of itssymmetry. This is important because the centers of lenses 30 and 32 areoff-set. The other aberrations of the lenses are corrected byconventional means, similar to those used with microscope objectives.

The improvement to be expected by this system can be evaluated asfollows:

The group delay for any ray propagating along a fiber of length L andrefractive index n is given by where 0 is the ray angle;

1' and a are constants. Thus, the delay, t, is proportional to 0 Thepower, dP, radiated from an isotropic point source between a cone withapex angle 0 and a cone with apex angle 0 d0 is proportional toTherefore, if an infinitely narrow pulse is launched into an uncorrectedmultimode optical fiber, the pulse deteriorates into a rectangular pulseof width 9, as

shown in FIG. 8, the dispersion of the material (i.e., as a function offrequency) being neglected.

Assuming that one equalizer is introduced at midpoint along the fiber,the total delay for the ray radiated at angle 0 is, according toequation (3), proportional to Omitting the constant 0 /4, the importantterm is (6 O /2), which is to be compared to the factor 0' obtainedwithout equalization. Substituting in (5), we obtain 1 dP/dt N2 (G /4) zunit, which is then spliced into the fiber transmission line using suchsplicing techniques as are disclosed, for example, in the copending US.Pat. application by E. A. J. Marcatili, Ser. No. 262,002, filed June 12,1972, or in the copending US. Pat. application by R. F. Trambarulo, Ser.No. 239,034, filed Mar. 29, 1972, and assigned to applicant's assignee.

A two-dimensional form of a ray inverter for use with ribbon fibers, ofthe tvpe shown in FIG. 2, can be realized by integrated opticstechniques. It is well known that the phase velocity of a wave guided bya thin film deposited on a substrate of lower refractive index decreasesas the thickness of the film increases, and that focusing effects can berealized by shaping the film thickness. (See, for example, Solid-StateSelf- Focusing Surface Waveguide (Microguide)" by Junichi Nishizawa andSkira Otsuka, Applied Physics Letters, July 15, 1972, p. 48.) Thus, anintegrated ray inverter constructed in accordance with these techniqueswould appear as illustrated in FIG. 10 wherein the thicker film regions100, 101 and 102 fonn the lens of the ray inverter. The film 103,deposited on a substrate 104 of cladding material, is typically of theorder of 3 .tm thick along the regions of uniform thickness and about 1mm wide. The thickness increases to about 5pm in the regions of thelenses. The use of integrated optic techniques makes it very easy andconvenient to stack together a plurality of such structures for use inmultichannel systems.

in all cases it is understood that the above-described arrangements areillustrative of a small number of the many possible specific embodimentswhich can represent applications of the principles of the invention.Numerous and varied other arrangements can readily be devised inaccordance with these principles by those skilled in the art withoutdeparting from the spirit and scope of the invention.

What is claimed is:

l. A delay equalizer for coupling optical wave energy between the endsof two longitudinally spaced, coax ially aligned, multimode opticalfibers comprising:

a sequence of three converging lenses equally spaced along the regionbetween said fibers;

the first and the third of said lenses, having focal lengths F/2,disposed with their optical centers located a distance F from theadjacent fiber ends and a distance FB' JZ away from the fiber axis,where 6' is the maximum angle at which wave energy, corresponding to thehighest order propagating mode, is emitted at the end of said fiber;

and the second of said lenses, having a focal length F, disposed withits optical center located along said fiber axis a distance F from eachof said other lenses. 2. The equalizer according to claim 1 wherein saidfibers include an inner core having a narrow dimension supportive ofonly a single mode of wave propagation, and a wide dimension supportiveof a plurality of propagating modes;

wherein said first and third lenses comprise two identical sections,each of which has an optical center which lies along a lineperpendicular to the wide dimension of said fiber core;

and wherein said second lens is a cylindrical lens whose optical centerlies along a line which intersects the fiber axis along a directionperpendicular to the wide dimension of said fiber.

3. The equalizer according to claim 1 wherein said fibers include acircular inner core supportive of a plurality of propagating modes;

wherein said first and third lenses are toroidal-like lenses whosephysical centers lie along the fiber axis, and whose optical centers liealong a circle of radius FE /2;

and wherein said second lens is a spherical lens whose physical andoptical centers lie along the fiber axis.

i i t

1. A delay equalizer for coupling optical wave energy between the endsof two longitudinally spaced, coaxially aligned, multimode opticalfibers comprising: a sequence of three converging lenses equally spacedalong the region between said fibers; the first and the third of saidlenses, having focal lengths F/2, disposed with their optical centerslocated a distance F from the adjacent fiber ends and a distance F theta''max/2 away from the fiber axis, where theta ''max is the maximum angleat which wave energy, corresponding to the highest order propagatingmode, is emitted at the end of said fiber; and the second of saidlenses, having a focal length F, disposed with its optical centerlocated along said fiber axis a distance F from each of said otherlenses.
 2. The equalizer according to claim 1 wherein said fibersinclude an inner core Having a narrow dimension supportive of only asingle mode of wave propagation, and a wide dimension supportive of aplurality of propagating modes; wherein said first and third lensescomprise two identical sections, each of which has an optical centerwhich lies along a line perpendicular to the wide dimension of saidfiber core; and wherein said second lens is a cylindrical lens whoseoptical center lies along a line which intersects the fiber axis along adirection perpendicular to the wide dimension of said fiber.
 3. Theequalizer according to claim 1 wherein said fibers include a circularinner core supportive of a plurality of propagating modes; wherein saidfirst and third lenses are toroidal-like lenses whose physical centerslie along the fiber axis, and whose optical centers lie along a circleof radius F theta ''max/2; and wherein said second lens is a sphericallens whose physical and optical centers lie along the fiber axis.